holt ca course 1 3-6 comparing and ordering rational numbers warm up warm up california standards...
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![Page 1: Holt CA Course 1 3-6 Comparing and Ordering Rational Numbers Warm Up Warm Up California Standards California Standards Lesson Presentation Lesson PresentationPreview](https://reader030.vdocuments.us/reader030/viewer/2022032611/56649e7a5503460f94b7b84d/html5/thumbnails/1.jpg)
Holt CA Course 1
3-6 Comparing and Ordering Rational Numbers
Warm UpWarm Up
California StandardsCalifornia Standards
Lesson PresentationLesson Presentation
PreviewPreview
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Holt CA Course 1
3-6 Comparing and Ordering Rational Numbers
Warm UpWrite each mixed number as an improper fraction.
1. 1
3. 1
74
238
116
34
56
2. 2 78
4. 8 9712
112
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Holt CA Course 1
3-6 Comparing and Ordering Rational Numbers
NS1.1 Compare and order positive and negative fractions, decimals, and mixed numbers and place them on a number line.Also covered: NS2.4
California Standards
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Holt CA Course 1
3-6 Comparing and Ordering Rational Numbers
Vocabulary
rational number
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Holt CA Course 1
3-6 Comparing and Ordering Rational Numbers
Which is greater, or ?79
29
To compare fractions with the same denominator, just compare the numerators.
79 > 2
9 because 7 > 2.= 7
9
=29
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Holt CA Course 1
3-6 Comparing and Ordering Rational Numbers
One way to compare fractions with unlike denominators is to use models. For example,
the models show that < . 38
12
Another way to compare fractions with unlike denominators is to first write equivalent fractions with common denominators. Then compare the fractions.
38= 1
2=
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Holt CA Course 1
3-6 Comparing and Ordering Rational Numbers
Compare the fractions. Write < or >.
Additional Example 1A: Comparing Fractions
79
58
The LCM of the denominators 9 and 8 is 72.
79 = 7 8
9 8 = 5672
58 = 5 9
8 9 = 4572
5672 > 45
72 , and so . 79 > 5
8
Write equivalent fractions with 72 as the denominator.
Compare the numerators.
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Holt CA Course 1
3-6 Comparing and Ordering Rational Numbers
Additional Example 1B: Comparing Fractions
Compare the fractions. Write < or >.
25
37
– –
25– = –2 7
5 7= –14
3537– = –3 5
7 5 =–15 35
– 1435 > – 15
35 , and so – > .25
– 37
Write equivalent fractions with 35 as the denominator.Put the negative signs in the numerators.
Both fractions can be written with a denominator of 35.
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Holt CA Course 1
3-6 Comparing and Ordering Rational Numbers
A fraction less than 0, such as , can be
written as , , or .
Helpful Hint!
2 52
52 5 2
5
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Holt CA Course 1
3-6 Comparing and Ordering Rational Numbers
Compare the fractions. Write < or >.
56
78
The LCM of the denominators 6 and 8 is 48.
56 = 5 8
6 8 = 4048
78 = 7 6
8 6 = 4248
4048 < 42
48 , and so . 56 < 7
8
Write equivalent fractions with 48 as the denominator.
Check It Out! Example 1A
Compare the numerators.
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Holt CA Course 1
3-6 Comparing and Ordering Rational Numbers
Compare the fractions. Write < or >.
68
57
– –
68– = –6 7
8 7= –42
5657– = –5 8
7 8 =–40 56
– 4256 < – 40
56 , and so – < .68
– 57
Write equivalent fractions with 56 as the denominator.Put the negative signs in the numerators.
Check It Out! Example 1B
Both fractions can be written with a denominator of 56.
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Holt CA Course 1
3-6 Comparing and Ordering Rational Numbers
To compare decimals, line up the decimal points and compare digits from left to right until you find the place where the digits are different.
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Holt CA Course 1
3-6 Comparing and Ordering Rational Numbers
Compare the decimals. Write < or >.
Additional Example 2A: Comparing Decimals
0.427 0.425
0.427
0.425
Since 0.007 > 0.005, 0.427 > 0.425.
Line up the decimal points.The tenths and hundredths arethe same.Compare the thousandths:
7
5
7 > 5.
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Holt CA Course 1
3-6 Comparing and Ordering Rational Numbers
Compare the decimals. Write < or >.
Additional Example 2B: Comparing Decimals
0.73 0.734
0.733…
0.734
Line up the decimal points.
The tenths and hundredths arethe same.
Compare the thousandths:
3
4
3 < 4.
0.73 =_
Since 0.003 is < 0.004, 0.73 < 0.734.
0.73 is a repeating decimal.
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Holt CA Course 1
3-6 Comparing and Ordering Rational Numbers
Compare the decimals. Write < or >.
0.535 0.538
0.535
0.538
Since 0.005 < 0.008, 0.535 < 0.538.
Line up the decimal points.The tenths and hundredths arethe same.Compare the thousandths:
5
8
5 < 8.
Check It Out! Example 2A
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Holt CA Course 1
3-6 Comparing and Ordering Rational Numbers
Compare the decimals. Write < or >.
Check It Out! Example 2B
0.334
0.3333…
0.334
Line up the decimal points.The tenths and hundredths arethe same.Compare the thousandths:
3
4
3 < 4.
0.3
Since 0.003 is < 0.004, 0.3 < 0.334.
0.3 = 0.3 is a repeating decimal.
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Holt CA Course 1
3-6 Comparing and Ordering Rational Numbers
A rational number is a number that can be written as a fraction or quotient of integers with a nonzero denominator. When rational numbers are written in a variety of forms, you can compare the numbers by writing them all in the same form.
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Holt CA Course 1
3-6 Comparing and Ordering Rational Numbers
The values on a number line increase as you move from left to right.
Remember!
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Holt CA Course 1
3-6 Comparing and Ordering Rational Numbers
Order
Additional Example 3: Ordering Fractions and Decimals
45
0.93, and 0.9 from least to greatest.,
45 = 0.80
Graph the numbers on a number line.
0 0.2 0.4 0.6 0.8 1
0.93
Write as decimals with the same number of places.
0.93 = 0.93 0.9 = 0.90
0.80 < 0.90 < 0.93 Compare the decimals.
45From least to greatest, the numbers are , 0.9, 0.93.
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Holt CA Course 1
3-6 Comparing and Ordering Rational Numbers
Order , 0.84, and 0.7 from least to greatest.
Check It Out! Example 3
35
35 = 0.60
Graph the numbers on a number line.
0 0.2 0.4 0.6 0.8 1
0.84
Write as decimals with the same number of places.
0.84 = 0.84 0.7 = 0.70
0.60 < 0.70 < 0.84 Compare the decimals.
35
From least to greatest, the numbers are , 0.7, 0.84.
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Holt CA Course 1
3-6 Comparing and Ordering Rational Numbers
Lesson Quiz
Compare the fractions. Write > or <.
1. 2.
Compare the decimals. Write < or >.
3. 0.32 and 0.312
>
37
and 410
58 and
23
<>
56
0.8, 0.826, 56
4. Order , 0.8, 0.826 from least to greatest.
Graph the numbers on a number line.
0.80 0.81 0.82 0.83 0.84 0.85
0.8 0.82656